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Design of curved Beams-B13

Data

1) Rdius of girder (beam) R 16.565 m

2) Width of Girder(beam) B 300 mm

3) Depth of the Girder (beam) D 700 mm4) Load on girder (beam) q 36 Kn/m

6) Angle q 30 Degree

7) Grade of concrete M 25 N/mm2

8) Grade of steel Fy 415 N/mm2

9) Number of columns which creates arc of full circle n 12 No

Table: Moment coefficient in circular Girders

Number

of

columns

Angle to the

center of

circle

Negative BM

at support

Positive BM at

Center span

Max

torque

Angular

distance for

torsion

n K1 K2 K3

4 90 deg 0.0342 0.0176 0.0053 19 deg-12 min

6 60 deg 0.0148 0.0075 0.0015 12 deg-44 min

8 45 deg 0.0083 0.0041 0.0006 9 deg-33 min

10 36 deg 0.0054 0.0023 0.0003 7 deg-30 min

12 30 deg 0.0037 0.0014 0.0017 7 deg-15 min

As per angle Max negative BM coeficient K1 0.0037

As per angle Max positive BM coeficient K2 0.0014

As per angle Max torsional BM coeficient K3 0.0017

As per table the torsion acting at a distance in deg Angle in deg 9.5

Loads

self weight of beam 5.25 Kn /m

UDL 36 Kn /m

Total design loads w 41.25 Kn /m

Total load on circular girder Wt (2 x p xR x w) 4293.213169 KN

Bending moment and shear forces

Max negative BM at support sections Mn K1xWtxR 263.1331817 KNm

Max positive BM at centre of support Mp K2xWtxR 99.5639066 KNm

Max torsional moment at an angle given in table from support T K3xWtXR 120.8990294 KNm

Max Shear force at support section V 178.884 KN

Max Shear force at section of max torsion Vt 65.59075674 KN

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Design of support section

Required depth d 617.5373975 mm

Provided depth 667 mm

Required depth is less than provided depth hence safe

Ultimate moment 394.6997726 KNm

Mu/Bd2

2.957290265

Pt from table pt 0.977

Ast 1954.977 mm2

steel required

Dia of bars used 25 mm

Area of steel 490.859375 mm2

No of bars required 3.982763903 no

No of bars provided 5

provide 5 nos of 25 mm dia bars 2454.296875 mm2

shear tv = v / b d 1.340958636 N/mm2

100 x Ast/bd 1.22653517

From table 23 of IS 456 code, permisible shear stress in conc- tc 0.64 N/mm2

tv is more than tc shear reinforcements are required

Hence shear reinforcement is required

Shear taken by concrete Vc=tc b d 128.064 KN

Balance shear Vs 50.820 KN

Use stirrups dia 10 mmspacing Sv 474.1623708 mm

Adopt 10 mmm dia 4legged vertical stirrups at 150 mm c/c

Design of mid span section

Ultimate moment 149.3458599 KNm

Mu/Bd2

1.118974695

Pt from table pt 0.338

Ast 676.338 mm2

But minimum area of steel is given by

As= (0.85Bd/fy) 409.8433735 mm2

Dia of bars used 25

Area of steel 490.859375

No of bars required 1.377865096

No of bars provided 4

provide 4 nos of 25 mm dia bars 1963.4375 mm2

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Design of section subjected to max Torsion and shear

Mt T(1+D/b)/1.7 286.8388738 KNm

Me=(M+Mt) ( in ring beam torsion is max where Bm is zero) 286.8388738

Ultimate moment 430.2583106Mu/Bd

23.223712811

Pt from table pt 1.104

Ast 2209.104 mm2

But minimum area of steel is given by

As= (0.85Bd/fy) 409.8433735 mm2

Dia of bars used 25

Area of steel 490.859375

No of bars required 0.58436059

No of bars provided 4

provide 4 nos of 25 mm dia bars 1963.4375 mm2

Equivalent shear Ve=(v+1.6T/b) 710.3855804 KN

tve=Ve/bd 3.550152826 N/mm2

100Ast/bd 0.981228136 N/mm2

From table 23 of IS 456 code, permisible shear stress in conc- tc 0.64 N/mm2

tv is more than tc shear reinforcements are required

dia of stirrups 10 mm

Area of steel 78.5375 mm2

using 10 mm four legged stirrups with side cover of 25mm

and bottom cover of 50 mmb1 250

d1 650

Asv 157.075 mm2

Sv= Asv sigsv(b1 d1/T+2.5d1/v) 49.4535681 mm

But Asv